Structural and interfacial stability of multiple solutions for stratified flow

Prediction of the liquid level in stratified two-phase upwards flow shows that one may have multiple solutions. In this case it is necessary to determine which solutions will actually occur and whether hysteresis is possible, namely whether it is possible to have two or more solutions for the same operating conditions. In this work the stability of the solutions for stratified flow is considered using two types of stability analyses: (1) structural stability analysis; and (2) interfacial stability analysis (Kelvin-Helmholtz, K-H). For the K-H stability analysis we used two methods: an approximate simplified method suggested by Taitel & Dukler; and a more rigorous method suggested by Barnea, which is based on a combination of the viscous K-H and inviscid K-H analyses. The results show that whenever three solutions exist only the first, i.e. the solution with the thinnest liquid level, is stable. The middle solution is always structurally unstable (linearly), whereas the third solution is structurally unstable to large disturbances (non-linear stability). The third solution is usually also unstable to the K-H type of instability. As a result it is concluded that hysteresis is not possible and that only the thinnest solution will be observed practically.